96
3 Forced Vibration of Single Degree of Freedom System
Fig. 3.24 Suddenly applied
load
The response is determined for two time ranges.
(i) t < t d
F (τ ) = F 0
From Eq. (3.91),
x =
t
0
F 0
mp
sin p (t − τ ) dτ =
F 0
k
(1 − cos pt)
At t = t d ,
x t d =
F 0
k
(1 − cos pt d )
and ˙
x t d =
F 0
k
( p sin pt d )
(a)
(ii) t > t d , F (τ ) = 0
From Eq. (3.92),
x = x t d cos p (t − t d ) +
˙
x t d
p
sin p (t − t d )
or
x =
F 0
k
(1 − cos pt d ) cos p (t − t d ) +
F 0
k
sin pt d sin p (t − t d )
or